UFD Questions

Hello all,

I have to questions regarding UFD's.

1. Assume that Q[Sqrt(d)] is a UFD and that is an integer in Q[Sqrt(d)] where and (with a bar above it) have no common factor, but the norm of , N[ ] is a perfect square in . Can someone show that is a perfect square in the quadratic integers in Q[Sqrt(d)] ?

1. Assume that Q[Sqrt(d)] is a UFD and that is an integer in Q[Sqrt(d)] where and (with a bar above it) have no common factor, but the norm of , N[ ] is a perfect square in . Can someone show that is a perfect square in the quadratic integers in Q[Sqrt(d)] ?